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My doctoral journey has been strenuous and arduous, yet alluring and memorable despite the sweating hardship and sleepless nights I endured. I take this opportunity to record my acknowledgement to those people who have helped me in one way or another along this long but fulfilling road.

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Above all, I would like to express my heartfelt appreciation to my supervisor, Professor Xavier Intes. He continually conveyed a spirit of unsurpassed and infectious enthusiasm in research and scholarship, which reinforced my conviction to pursue scientific excellence. I am grateful for his persistent support and thoughtful guidance, which are essential to the completion of the present work. His understanding, warm encouragement and ongoing confidence in me tremendously helped me tackle difficulties and conquer frustration at key moments. His high standards will have a remarkable influence on my entire career path.

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Next I give my sincere gratitude to my committee members, Professors George Xu, Stanley Dunn, Frederic Lesage, and David Boas. I thank Professor George Xu for teaching me fundamental knowledge of various imaging modalities, from which I generalize and analogize the principle of optical imaging systems. Without Professor Stanley Dunn pointing out the importance of understanding the vision and basics, I would not be able to take a step back to the critical concepts, define the problem and clarify the motivation and goal of this study. Professor Frederic Lesage's work on widefield illumination in slabs inspired me the approach to extend the mathematical model on arbitrary geometry, and his helpful suggestions on statistics method have been of great value in this work. I thank Professor Boas for his early work that sparked my interest in mathematical modeling, and his insightful discussions on the state of the art of time-domain imaging, inverse models, and parallel computing. Without their guidance and help this dissertation would not have been possible.

To my labmate Dr. Vivek Venugopal, I am extremely grateful for his extensive discussion and constructive comments on my projects, as well as his kind and compassionate care and support over the years. Especially, without him I would not be able to finish the experiment validation of my theory, which is a critically important part of my thesis. I also thank Monish Pimpalkhare for providing me the spine model, and wish him good luck in his future endeavors.

Moreover, it was an honor to work with Dr. Qianqian Fang at the Martinos Center for Biomedical Imaging at Harvard Medical School, for his expertise extended to me in the development of the mesh-based software. His enthusiasm for scientific computing will have lasting impact on me. I would also like to acknowledge the technical support of the Computational Center for Nanotechnology Innovations (CCNI), particularly in the detailed  guidance for using the massively parallel computing environment and related software. Adam Todorski and Cameron Smith, deserve special mention.

I am indebted to all the professors who taught me in Rensselear Polytechnic Institute, for providing a stimulating environment in which I grew intellectually and personally. Professors Fengyan Li and Kristin Bennett from the Department of Mathematics were especially helpful, for patiently guiding me to apply advanced linear algebra and optimization methods to real world applications. 

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Finally, I would like to thank my parents Kezhong Chen, Xiulan Pan,  my grand-father Yuansong Chen, and Dr. Yun Jing, who gave me unequivocal moral support and great patience throughout, for which my mere expression of thanks likewise does not suffice. Thanks for encouraging me to explore the principles of nature and to be independent thinkers when I was little, and for their confidence in me which enhanced my ability to succeed in my academic career. Without their help it would have been impossible for me to achieve this stage of high education. To them I dedicate this thesis. 